456480 has 72 divisors (see below), whose sum is σ = 1562652. Its totient is φ = 121344.

The previous prime is 456461. The next prime is 456499. The reversal of 456480 is 84654.

456480 = T₈₆ + T₈₇ + ... + T₁₄₉.

456480 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (456461) and next prime (456499).

It can be written as a sum of positive squares in 2 ways, for example, as 404496 + 51984 = 636^2 + 228^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1282 + ... + 1598.

2⁴⁵⁶⁴⁸⁰ is an apocalyptic number.

456480 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 456480, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (781326).

456480 is an abundant number, since it is smaller than the sum of its proper divisors (1106172).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

456480 is a wasteful number, since it uses less digits than its factorization.

456480 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 338 (or 327 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 456480 is about 675.6330364924. The cubic root of 456480 is about 76.9970201804.

Adding to 456480 its product of nonzero digits (3840), we get a triangular number (460320 = T₉₅₉).

It can be divided in two parts, 45 and 6480, that multiplied together give a square (291600 = 540²).

The spelling of 456480 in words is "four hundred fifty-six thousand, four hundred eighty".